Physics Investigation of Gymnastics

The iron cross is one of the most difficult skills on the rings. To
practice, we sometimes use a pulley strap to help support. Or, one could use the strap that hold the rings and pull it out so that it
would support part of our arm while attempting the iron cross. When one sees
gymnasts in the Olympic do the Iron Cross, do they really hold the iron cross with a ninety degree angle formed with the arms and his torso? A physics investigation of the iron cross would explain.

Here is an article from Boston University:

Although many people do not realize it, physics is involved
in every aspect of life. Gymnastics is one of many sports
that is performed by combining the machinery of the human
body and basic physics. One particular example is the ring
exercise. The body of a gymnast performing the ring exercise
is subject to extreme stress, coped with by an integration of
physics and biology. Although many elements of physics are
incorporated into performing this procedure, I will primarily
focus on one in particular- tension. By applying Newton's
second law under equilibrium conditions, I will examine the
question of whether or not the perfect "iron cross" maneuver
on the ring exercise is physically attainable. Do you think a
gymnast can support his weight on the rings having his arms
form a perfect ninety degree angle with his torso?

The basic formulas I will use to answer the aforementioned
question are as follows:

The net force in the x direction = 0

The net force in the y direction = 0

By combining these simple equations with basic
trigonometry, I will solve the problem.

The conditions for the problem I will solve are as follows: a
655 Newton gymnast is suspended in air by holding on to the
rings. However, the rings are not the focus of the problem,
because the object upon or with which the gymnast supports
himself is not under examination. (In fact, one could
substitute two solid surfaces or two bars for the rings.) If the
gymnast were to hold on to the rings so as to create 60 degree
angles between his armpits and a plane just below his armpits
which is parallel to the ground, what would the tension have
to be in his arms to support his weight? Assuming equilibrium
in the y direction:

Tsin 60 + Tsin 60 -655= 0--->2Tsin 60 =655-->T=378.2 N
What if the gymnast were to create 35 degree
angles between his armpits and the imaginary plane, what
then would be the necessary tension in each arm?

As you can see, the closer the gymnast gets to forming angles
of zero degrees between his armpits and the imaginary plane,
the stress (in the form of tension) applied to his arms
increases significantly. This is simply because as the angle
decreases, so does the value of the sine function of the angle.
In order to compensate for the decreased sine value, the
tension force is increased. Eventually, the tension required in
each arm will become impossible to sustain. I will solve for
the tensions required for two more angles to demonstrate this
point. If the angles were 2 degrees:

Tsin 2 + Tsin 2 -655=0----> T= 9384.1 N

If the angles were .001 degrees:

Tsin .001 + Tsin .001 - 655=0----> T=18764367.8 N

In conclusion, it is obvious that this enormous tension is
unsustainable by the human arm. This fact, however, does not
diminish the fact that gymnast's do possess superior strength.
Although it is physically impossible to perform the perfect
"iron cross," the human eye cannot easily perceive this
inability. For when one watches a world-class gymnast
perform this maneuver, it is often far from obvious that his
arms are not exactly perpendicular to his torso.